Kinetically limited valence of colloidal particles with surface mobile DNA linkers

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Kinetically limited valence of colloidal particles

with surface mobile DNA linkers

Pedro A. S´anchez∗

Computational and Soft Matter Physics, Faculty of Physics, University of Vienna, 1090 Vienna, Austria

Alessio Caciagli

Former aﬃliated: Department of Physics, University of Cambridge, Cambridge, CB3 0HE, United Kingdom

Soﬁa S. Kantorovich

Computational and Soft Matter Physics, Faculty of Physics, University of Vienna, 1090 Vienna, Austria

Research Platform MMM Mathematics-Magnetism-Materials, Vienna, Austria

Erika Eiser

Department of Physics, Norwegian University of Science and Technology, 7491 Trondheim, Norway

Department of Physics, University of Cambridge, Cambridge, CB3 0HE, United Kingdom

Abstract

We characterize the self-assembly of colloidal particles with surface mobile DNA linkers under kinetically limited valence

conditions. For this, we put forward a computer simulation model that captures quantitatively the interplay between the

main dynamic processes governing these systems and allows the simulation of the long time scales reached in experiments.

The model is validated by direct comparison with available experimental results, showing an overall good agreement

that includes measurements of the average eﬀective valence and its probability distribution as a function of the density

of DNA linkers on the particles surface. Finally, simulation results are used to evidence the opposite impact of particle

density and characteristic DNA hybridization time on the eﬀective valence.

1. Introduction

Current experimental techniques allow the synthesis of

colloidal particles with ﬁnely tuned selectivity and di-

rectionality of their bonding interactions. This makes

such particles outstanding potential building blocks for

the rational design of material created by hierarchical self-

assembly [1–5]. One of the most interesting strategies to

design colloidal particles with directed self-assembly prop-

erties is based on their surface functionalization with DNA

strands of selected base sequences. The bonding interac-

tions of such DNA-coated colloids (DNACCs) are there-

fore mediated by DNA hybridization of complementary

strands, which act as crosslinkers [6–9]. The thermo-

reversibility and high speciﬁcity of DNA hybridization

provides precise temperature control of the colloidal self-

assembly and a very ﬂexible mechanism to tune the result-

ing structures and rheological properties [10–15].

∗Corresponding author

Email address: pedro.sanchez@univie.ac.at (Pedro A.

S´anchez)

Most early works on directed self-assembly of DNACCs

were focused on the crystallization of solid core particles

functionalized with arrangements of DNA linkers anchored

to ﬁxed points of their surfaces, ﬁrst using nanoparticles

[16, 17] and later larger colloidal particles as solid cores

[18–21]. In the latter case, crystallization turned out to

be more diﬃcult due to the relatively shorter range of the

DNA crosslinking interaction with respect to the parti-

cle size. This leads to rather rigid interparticle bonds and,

therefore, to a higher tendency to form kinetically trapped

amorphous aggregates [14, 22, 23]. Thus, regular struc-

tures of large colloidal particles have to be obtained by

controlling the balance of binding/unbinding processes of

the DNA linkers, so that reconﬁgurations of the aggregates

by means of ‘rolling motions’ of the bonded particles (i.e.,

orbit-like relative movements) can take place [21, 24]. This

also requires a large and homogeneous enough surface cov-

erage of linkers [24]. Nevertheless, dynamics of this crys-

tallization process tend to be very slow [19], diﬃculting

any large scale production.

The aforementioned limitations stimulated the explo-

ration of novel strategies for the design of DNACCs.

arXiv:2210.14209v1 [cond-mat.soft] 25 Oct 2022

One of such approaches is the usage of soft materials as

core particles. Currently there is a pletora of soft core

DNACCs, including microemulsion droplets [25–30] vesi-

cles [31, 32] and supramolecular DNA nanostructures [33].

This opened up the possibility to create soft materials of

high technological interest, such as thermo-reversible gels

with tunable properties [34]. Another important recent

development is the synthesis of DNACCs with on-surface

mobile linkers, i.e., systems in which the anchoring points

of the DNA chains can diﬀuse on the surface of the core

particle. For solid cores this is achieved by coating them

with a non-rigid interface, such as a lipid bilayer, to which

the linkers are attached [35]. Many soft core particles,

such as droplets, vesicles and micelles, have non-rigid in-

terfaces that make linkers attached to them naturally mo-

bile [28, 34, 36]. Importantly, such mobility is not limited

to unbinded linkers, as already established crosslinkers can

still diﬀuse on the surface of the particles they bind. Sur-

face diﬀusion tends to smear out inhomogeneities in the

distribution of free linkers and allows rolling motions of

the bonded particles without the need of any unbinding

process, lighting up the conditions and time scales for crys-

tallization. In addition, mobile linkers provide additional

ways to control the valence of the particles [37, 38] and

ease the design of sophisticated sequential self-assembly

schemes [39].

The advantages brought by the on-surface mobility of

the linkers in DNACCs come at the cost of a more chal-

lenging theoretical characterization than the one required

by their rigidly anchored counterparts. This, together with

their earlier development, made the latter the main subject

of theoretical studies on DNACCs, frequently addressed

as a particular case of ligand-receptor assembling systems

[38, 40–44]. In general, such studies have been focused

on the binding/unbinding dynamics of the linkers, as the

main parameter determining the ﬁnal assembled structure,

and the strategies to avoid kinetically arrested conﬁgura-

tions [22, 23, 25, 38, 43–50]. Except for some favorable

limit cases—i.e., systems with linker lengths comparable

to core sizes and very low number of linkers [51, 52]—most

theortical models for DNACCs self-assembly rely on inter-

particle eﬀective potentials that avoid any explicit linker

representation [39, 42, 50]. Eﬀective potentials are ﬁtted

to experimental data on the basis of conﬁgurational en-

ergy and combinatorial entropy considerations [37, 53–55].

However, in systems with surface mobile linkers, the in-

terplay of the aforementioned processes with the diﬀusion

of the linkers becomes determinant. The basic features of

this interplay have been discussed in few pioneering works,

mainly as a qualitative generalization of the ﬁndings ob-

tained from speciﬁc experimental systems [28, 29], whereas

eﬀorts towards a comprehensive theoretical characteriza-

tion are still very scarce. Bachmann and co-workers pre-

sented an extension of the combinatorial thermodynamic

approaches developed for systems with rigidly attached

linkers to include two essential aspects of the kinetics of

mobile linkers: ﬁrst, the ﬁnite rate of linker binding pro-

cesses and, second, the extinction of such processes once all

available linkers become bonded. As a consequence of the

competition between this model binding kinetics and the

diﬀusion of the core particles, formation of clusters with

very low average coordination number, or valence, was

predicted [43]. However, as diverse experimental works

have evidenced, this ﬁts only to very dilute systems with

very low surface densities of linkers, whereas more compact

structures are obtained as particle and linker densities are

increased [28, 56]. In one of such works, McMullen and

co-workers used their experimental results to develop a

two-fold phenomenological modelling approach that takes

the experimental probability distributions for the coordi-

nation numbers as ﬁtting parameters [56]. A very recent

work of this experimental group has addressed the self-

assembly under thermodynamic equilibrium conditions—

i.e., for temperatures around the hybridization threshold,

Th, corresponding to the binding/unbinding transition,

and large concentrations of particles and linkers [57]. How-

ever, to our best knowledge, no theoretical study to date

has been able to predict the structures observed in experi-

ments under kinetically controlled self-assembly conditions

directly from the physical properties of the system [56]. In

this work we present a minimal computer simulation model

for the stable self-assembly of micron-sized DNACCs with

surface mobile linkers that, for the ﬁrst time, takes into ac-

count all the relevant dynamic processes governing these

systems and considers the time dependence of the eﬀective

interactions. Despite the model was originally aimed at the

qualitative description of the interplay of such processes,

it is able to provide quantitative predictions in reasonably

good agreement with available experimental results.

2. System qualitative description

Fig. 1 sketches the basic structure of DNACCs with sur-

face mobile linkers and the main dynamic processes in-

volved in their self-assembly. Typically, surface mobile

DNA linkers are hybrid molecules consisting of a single

strand DNA segment (ss-DNA) with prescribed sequence,

a double strand DNA segment (ds-DNA) that acts as a

semiﬂexible stem of the former and an anchor molecule

adsorbed on the surface of the core particle (see Fig. 1b).

The simplest self-assembling system one can make out of

core particles functionalized with such mobile linkers is a

binary symmetric suspension in which half of the parti-

cles carry linkers with a given ss-DNA sequence, A, and

the other half carry the corresponding complementary se-

quence, A0, being otherwise fully equivalent. Without loss

of generality, here we will use our model to address such

simple symmetric AA0self-assembling system, following

the experiments of reference [56]. In addition, we will focus

on stable self-assembly conditions only, i.e., at tempera-

tures well below the threshold hybridization temperature,

TTh.

For an initially homogeneous system, diﬀusion will bring

pairs of AA0particles into a close range. This will allow

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摘要：

KineticallylimitedvalenceofcolloidalparticleswithsurfacemobileDNAlinkersPedroA.SanchezComputationalandSoftMatterPhysics,FacultyofPhysics,UniversityofVienna,1090Vienna,AustriaAlessioCaciagliFormeraliated:DepartmentofPhysics,UniversityofCambridge,Cambridge,CB30HE,UnitedKingdomSoaS.KantorovichCompu...

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Kinetically limited valence of colloidal particles with surface mobile DNA linkers

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