Chain-Length-Dependent Correlated Molecular Motion in Polymers

We show how dynamic heterogeneities (DHs), a hallmark of glass-forming materials, depend on chain flexibility and chain length in polymers. For highly flexible polymers, a relatively large number of monomers ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>N</a:mi> <a:mi>c</a:mi> </a:msub> <a:mo>∼</a:mo> <a:mn>500</a:mn> </a:math> ) undergo correlated motion at the glass transition temperature ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>T</c:mi> <c:mi>g</c:mi> </c:msub> </c:math> ), independent of molecular weight ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>M</e:mi> </e:math> ). In contrast, less flexible polymers show a complex <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>N</g:mi> <g:mi>c</g:mi> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mi>M</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> behavior divided into three regimes, consistent with observations in both <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>T</k:mi> <k:mi>g</k:mi> </k:msub> <k:mo stretchy="false">(</k:mo> <k:mi>M</k:mi> <k:mo stretchy="false">)</k:mo> </k:math> and chain conformational structure. For short oligomers ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mo>≲</o:mo> <o:mn>2</o:mn> </o:math> Kuhn steps), a transition from mainly intermolecular correlations and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>N</q:mi> <q:mi>c</q:mi> </q:msub> <q:mo>∼</q:mo> <q:mn>200</q:mn> </q:math> to strongly intramolecular correlations and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>N</s:mi> <s:mi>c</s:mi> </s:msub> <s:mo><</s:mo> <s:mn>50</s:mn> </s:math> (roughly the molecular size) is observed; for longer chains, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>N</u:mi> <u:mi>c</u:mi> </u:msub> </u:math> increases weakly, before saturating. For poly(methyl methacrylate), a remarkable similarity is found between <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>N</w:mi> <w:mi>c</w:mi> </w:msub> <w:mo stretchy="false">(</w:mo> <w:mi>M</w:mi> <w:mo stretchy="false">)</w:mo> </w:math> and the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>M</ab:mi> </ab:math> -dependent ratio of the activation barriers of the structural ( <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>α</cb:mi> </cb:math> ) and secondary ( <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>β</eb:mi> </eb:math> ) relaxations; we present evidence that this relationship is a general feature of glass-forming polymers. Our results suggest a direct link between the DH length scale and the number of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>β</gb:mi> </gb:math> relaxation events jointly activated to facilitate the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>α</ib:mi> </ib:math> relaxation.